Elements Of Physical Chemistry
Elements Of Physical Chemistry
7th Edition
ISBN: 9780198796701
Author: ATKINS, P. W. (peter William), De Paula, Julio
Publisher: Oxford University Press
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Chapter 9, Problem 9B.3E
Interpretation Introduction

Interpretation:

Increasing order of bond length of the given species has to be arranged and also the bond order of each has to be identified.

Concept Introduction:

Molecular orbital (MO) theory is a method of determining molecular structure in which electrons are not assigned to individual bonds between atoms, but are treated as moving under the influence of the nuclei in the whole molecule.

According to this theory there are two types of orbitals,

  1. (1) Bonding orbitals
  2. (2) Antibonding orbitals

Electrons in molecules are filled in accordance with the energy; the anti-bonding orbital has more energy than the bonding orbitals.

The electronic configuration of oxygen molecule O2 can be represented as follows,

(σ1s)2(σ*1s)2(σ2s)2(σ*2s)2(σ2p)2( π2p)4( π*2p)2 

The symbol * represent the antibonding orbital

Sigma (σ) bonds are the bonds in which shared hybrid orbital’s electron density are concentrated along the internuclear axis.

Pi (π) bonds are the bonds in which shared un-hybridized orbital’s (p, d, etc.) electron density are concentrated in above and below of the plane of the molecule.

Bond order: It is the measure of number of electron pairs shared between two atoms.

Bondorder=12(NumberofelectronsinbondoingMOs-NumberofelectronsinantibondingMOs)

Bond length is inversely proportional to the bond order.

Atoms with unpaired electrons are called Paramagnetic. Paramagnetic atoms are attracted to a magnet.

Atoms with paired electrons are called diamagnetic. Diamagnetic atoms are repelled by a magnet

Expert Solution & Answer
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Explanation of Solution

  • Given species: O2+

There are 15 electrons in O2+. According to the MO theory its electron configuration can be written as,

(σ1s)2(σ*1s)2(σ2s)2(σ*2s)2(σ2p)2( π2px)2( π2py)2( π*2px)1 

MO diagram for O2+ ion can be drawn as follows,

(σ*2pz)(Antibondingelectrons)(π*2px)(π*2py)2px2py2pz2px2py2pz(π2px)(π2py)(Bondingelectrons)(σ2pz)

  (Antibondingelectrons)(σ2s)*2s2s(Bondingelectrons)(σ2s)2

  (Antibondingelectrons)(σ1s)*1s1s(Bondingelectrons)(σ1s)2

O2+Bondorder=12(NumberofelectronsinbondoingMOs-NumberofelectronsinantibondingMOs)=10-52=2.5

  • Given species: O2

There are 16 electrons in O2. According to the MO theory its electron configuration can be written as,

O2:(σ1s)2(σ*1s)2(σ2s)2(σ*2s)2(σ2p)2( π2px)2( π2py)2( π*2px)1 ( π*2py)1

O2Bondorder=12(NumberofelectronsinbondoingMOs-NumberofelectronsinantibondingMOs)=10-62=2

  • Given species: O2

There are 17 electrons in O2 one electron is added to the anti-bonding orbital. According to the MO theory its electron configuration can be written as,

O2:(σ1s)2(σ*1s)2(σ2s)2(σ*2s)2(σ2p)2( π2px)2( π2py)2( π*2px)2 ( π*2py)1

O2Bondorder=12(NumberofelectronsinbondoingMOs-NumberofelectronsinantibondingMOs)=10-72=1.5

  • Given species: O22

There are 18 electrons in O22. According to the MO theory its electron configuration can be written as,

O22:(σ1s)2(σ*1s)2(σ2s)2(σ*2s)2(σ2p)2( π2px)2( π2py)2( π*2px)2 ( π*2py)2

Bond order of O2 molecule and O2+ ion can be calculated as follows,

O22Bondorder=12(NumberofelectronsinbondoingMOs-NumberofelectronsinantibondingMOs)=10-82=1

Therefore,

The bond order decreases as follows,

Bondorder:O2+>O2>O2>O222.5>2>1.5>1

Bond order is inversely proportional to bond length.

Thus, increasing bond length is,

Bondlength:O2+<O2<O2<O22

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